Numerical study of vibrations of a nonlinear mechanical system simulating a cracked body

Bovsunovskii, A. P.

doi:10.1007/bf02510893

Cited by 19 publications

(16 citation statements)

References 3 publications

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“…However, it is difficult to determine the damping ratio with sufficient accuracy to estimate the correlations with the temperature, as reported in previous studies [8,19,21]. In addition, the cracks in a structure not only affect the structural stiffness [8,22,23] but also lead to variations in the structural damping ratio because of the appearance of plastic zones along the edges of the cracks [21]. Curadelli et al [24] showed the difference in the instantaneous damping coefficient between the healthy and damaged condition of a reinforced concrete beam.…”

Section: Variation In Dampingmentioning

confidence: 94%

Long-Term Vibration Monitoring of the Effects of Temperature and Humidity on PC Girders with and without Fly Ash considering ASR Deterioration

Fukada

Torii

2017

Shock and Vibration

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Structural responses have been used as inputs in the evaluation procedures of civil structures for years. Apart from the degradation of a structure itself, changes in the environmental conditions affect its characteristics. For adequate maintenance, it is necessary to quantify the environment-induced changes and discriminate them from the effects due to damage. This study investigates the variation in the vibration responses of prestressed concrete (PC) girders, which were deteriorated because of the alkali-silica reaction (ASR), concerning ambient temperature and humidity. Three PC girders were exposed to outdoor weather conditions outside the laboratory, one of which had a selected amount of fly ash in its mixture to mitigate the ASR. The girders were periodically vibration tested for one and a half years. It was found that when the temperature and humidity increased, the frequencies and damping ratios decreased in proportion. No apparent variation in the mode shapes could be identified. A finite element model was proposed for numerical verification, the results of which were in good agreement with the measured changes in the natural frequencies. Moreover, the different dynamic performances of the three specimens indicated that the fly ash significantly affected the vibrations of the PC girders under ASR deterioration.

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Section: Variation In Dampingmentioning

confidence: 94%

Long-Term Vibration Monitoring of the Effects of Temperature and Humidity on PC Girders with and without Fly Ash considering ASR Deterioration

Fukada

Torii

2017

Shock and Vibration

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“…Bovsunovskii [24] has obtained the general patterns of appearance of higher harmonics of the Fourier expansion of time dependence of vibration of a cracked body model by using the bilinear restoring force model, and, further, the author [25] has found that the level of nonlinear distortions is one of the most damage sensitive indicators. Chondros et al [26] have studied the dependency of the eigenfrequency changes due to a breathing edge-crack on the bilinear character of a beam.…”

Section: Introductionmentioning

confidence: 99%

Analysis of bilinear oscillators under harmonic loading using nonlinear output frequency response functions

Peng

Lang

Billings

et al. 2007

International Journal of Mechanical Sciences

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In this paper, the new concept of Nonlinear Output Frequency ResponseFunctions (NOFRFs) is extended to the harmonic input case, an input-independent relationship is found between the NOFRFs and the Generalized Frequency Response Functions (GFRFs). This relationship can greatly simplify the application of the NOFRFs.Then, beginning with the demonstration that a bilinear oscillator can be approximated using a polynomial type nonlinear oscillator, the NOFRFs are used to analyze the energy transfer phenomenon of bilinear oscillators in the frequency domain. The analysis provides insight into how new frequency generation can occur using bilinear oscillators and how the sub-resonances occur for the bilinear oscillators, and reveals that it is the resonant frequencies of the NOFRFs that dominate the occurrence of this well-known nonlinear behaviour. The results are of significance for the design and fault diagnosis of mechanical systems and structures which can be described by a bilinear oscillator model.

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“…In the above works, the possibility of change in damping level as a result of crack initiation was not taken into account [24]. At the same time, the suppressing influence of damping on nonlinear effects was pointed out, e.g., in [5,25,26]. It follows that when studying the interrelation between damage parameters and nonlinear-effect parameters, the change in damping level in the system because of crack initiation and growth must be taken into account.…”

mentioning

confidence: 98%

Comparative analysis of nonlinear resonances of a mechanical system with unsymmetrical piecewise characteristic of restoring force

Bovsunovskii

2007

Strength Mater

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We present results of a numerical comparative analysis of superharmonic resonances of the order 2/1-1/5 and subharmonic resonance of the order 1/2 of a mechanical single degree-of-freedom vibrating system with unsymmetrical characteristic of restoring force at different ratios of system rigidities in half-cycles and under the conditions of considerable change in vibration damping level in the system. Keywords: closing crack, sub-and superharmonic resonance, vibration spectrum, diagnostic signs of damage.Introduction. In the case of cyclic deformation of an elastic body, fatigue crack has the property of opening in the extension half-cycle and closing in the compression half-cycle (closing crack). At the instants of crack closure and opening, an abrupt change in the rigidity of the body takes place, which gives rise to a considerable nonlinearity of its dynamic behavior and, as a consequence, to the so-called nonlinear effects, to which sub-and superharmonic (nonlinear) resonances belong, as well as to nonlinearity of the vibrational response of the mechanical system (displacement, velocity, acceleration, strain, etc.) in resonant regimes of vibration.Periodic change in the rigidity of a mechanical system gives rise to a number of difficulties, which arise in the analytical solution of the problem of its forced vibrations. Approximate analytical solutions [1][2][3][4][5][6][7] are limited by simplifying assumptions of the properties of vibrating system and consider one or two nonlinear resonances, which makes it impossible to perform a comparative analysis of super-and subharmonic resonances of different order. The order of nonlinear resonance is determined by the number of super-or subharmonic in the vibration spectrum, whose amplitude increases monotonically as its frequency approaches the eigenfrequency of the vibrating system and reaches a maximum when these frequencies coincide. The superficial resemblance of the phenomenon to resonance determined its name -nonlinear resonance.In [5][6][7][8][9] consider superresonance of second order and [10, 11] subharmonic resonance of the order f p

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Numerical study of vibrations of a nonlinear mechanical system simulating a cracked body

Cited by 19 publications

References 3 publications

Long-Term Vibration Monitoring of the Effects of Temperature and Humidity on PC Girders with and without Fly Ash considering ASR Deterioration

Long-Term Vibration Monitoring of the Effects of Temperature and Humidity on PC Girders with and without Fly Ash considering ASR Deterioration

Analysis of bilinear oscillators under harmonic loading using nonlinear output frequency response functions

Comparative analysis of nonlinear resonances of a mechanical system with unsymmetrical piecewise characteristic of restoring force

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